Item 18 (005U) — The Clowder Project

Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
Style 4	`book`	Computer Modern	`amsthm`

Interaction With Powersets and Vector Spaces II. If $X$ is finite, then:
1. The set of singletons sets on the elements of $X$ forms a basis for the $\mathbb {F}_{2}$-vector space $\webleft (\mathcal{P}\webleft (X\webright ),\alpha _{\mathcal{P}\webleft (X\webright )}\webright )$ of Item 17.
2. We have
  \[ \dim \webleft (\mathcal{P}\webleft (X\webright )\webright )=\# \mathcal{P}\webleft (X\webright ). \]

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